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crypto: GnuPG based MPI lib - source files (part 1)
[linux-2.6/linux-acpi-2.6/ibm-acpi-2.6.git] / lib / mpi / mpih-div.c
blob87ede162dfabee78a4cad86e850fdefa06f622f8
1 /* mpihelp-div.c - MPI helper functions
2 * Copyright (C) 1994, 1996 Free Software Foundation, Inc.
3 * Copyright (C) 1998, 1999 Free Software Foundation, Inc.
4 *
5 * This file is part of GnuPG.
6 *
7 * GnuPG is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or
10 * (at your option) any later version.
11 *
12 * GnuPG is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with this program; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
20 *
21 * Note: This code is heavily based on the GNU MP Library.
22 * Actually it's the same code with only minor changes in the
23 * way the data is stored; this is to support the abstraction
24 * of an optional secure memory allocation which may be used
25 * to avoid revealing of sensitive data due to paging etc.
26 * The GNU MP Library itself is published under the LGPL;
27 * however I decided to publish this code under the plain GPL.
28 */
29
30 #include "mpi-internal.h"
31 #include "longlong.h"
32
33 #ifndef UMUL_TIME
34 #define UMUL_TIME 1
35 #endif
36 #ifndef UDIV_TIME
37 #define UDIV_TIME UMUL_TIME
38 #endif
39
40 /* FIXME: We should be using invert_limb (or invert_normalized_limb)
41 * here (not udiv_qrnnd).
42 */
43
44 mpi_limb_t
45 mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
46 mpi_limb_t divisor_limb)
47 {
48 mpi_size_t i;
49 mpi_limb_t n1, n0, r;
50 int dummy;
51
52 /* Botch: Should this be handled at all? Rely on callers? */
53 if (!dividend_size)
54 return 0;
55
56 /* If multiplication is much faster than division, and the
57 * dividend is large, pre-invert the divisor, and use
58 * only multiplications in the inner loop.
59 *
60 * This test should be read:
61 * Does it ever help to use udiv_qrnnd_preinv?
62 * && Does what we save compensate for the inversion overhead?
63 */
64 if (UDIV_TIME > (2 * UMUL_TIME + 6)
65 && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
66 int normalization_steps;
67
68 count_leading_zeros(normalization_steps, divisor_limb);
69 if (normalization_steps) {
70 mpi_limb_t divisor_limb_inverted;
71
72 divisor_limb <<= normalization_steps;
73
74 /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
75 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
76 * most significant bit (with weight 2**N) implicit.
77 *
78 * Special case for DIVISOR_LIMB == 100...000.
79 */
80 if (!(divisor_limb << 1))
81 divisor_limb_inverted = ~(mpi_limb_t) 0;
82 else
83 udiv_qrnnd(divisor_limb_inverted, dummy,
84 -divisor_limb, 0, divisor_limb);
85
86 n1 = dividend_ptr[dividend_size - 1];
87 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
88
89 /* Possible optimization:
90 * if (r == 0
91 * && divisor_limb > ((n1 << normalization_steps)
92 * | (dividend_ptr[dividend_size - 2] >> ...)))
93 * ...one division less...
94 */
95 for (i = dividend_size - 2; i >= 0; i--) {
96 n0 = dividend_ptr[i];
97 UDIV_QRNND_PREINV(dummy, r, r,
98 ((n1 << normalization_steps)
99 | (n0 >>
100 (BITS_PER_MPI_LIMB -
101 normalization_steps))),
102 divisor_limb,
103 divisor_limb_inverted);
104 n1 = n0;
105 }
106 UDIV_QRNND_PREINV(dummy, r, r,
107 n1 << normalization_steps,
108 divisor_limb, divisor_limb_inverted);
109 return r >> normalization_steps;
110 } else {
111 mpi_limb_t divisor_limb_inverted;
112
113 /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
114 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
115 * most significant bit (with weight 2**N) implicit.
116 *
117 * Special case for DIVISOR_LIMB == 100...000.
118 */
119 if (!(divisor_limb << 1))
120 divisor_limb_inverted = ~(mpi_limb_t) 0;
121 else
122 udiv_qrnnd(divisor_limb_inverted, dummy,
123 -divisor_limb, 0, divisor_limb);
124
125 i = dividend_size - 1;
126 r = dividend_ptr[i];
127
128 if (r >= divisor_limb)
129 r = 0;
130 else
131 i--;
132
133 for (; i >= 0; i--) {
134 n0 = dividend_ptr[i];
135 UDIV_QRNND_PREINV(dummy, r, r,
136 n0, divisor_limb,
137 divisor_limb_inverted);
138 }
139 return r;
140 }
141 } else {
142 if (UDIV_NEEDS_NORMALIZATION) {
143 int normalization_steps;
144
145 count_leading_zeros(normalization_steps, divisor_limb);
146 if (normalization_steps) {
147 divisor_limb <<= normalization_steps;
148
149 n1 = dividend_ptr[dividend_size - 1];
150 r = n1 >> (BITS_PER_MPI_LIMB -
151 normalization_steps);
152
153 /* Possible optimization:
154 * if (r == 0
155 * && divisor_limb > ((n1 << normalization_steps)
156 * | (dividend_ptr[dividend_size - 2] >> ...)))
157 * ...one division less...
158 */
159 for (i = dividend_size - 2; i >= 0; i--) {
160 n0 = dividend_ptr[i];
161 udiv_qrnnd(dummy, r, r,
162 ((n1 << normalization_steps)
163 | (n0 >>
164 (BITS_PER_MPI_LIMB -
165 normalization_steps))),
166 divisor_limb);
167 n1 = n0;
168 }
169 udiv_qrnnd(dummy, r, r,
170 n1 << normalization_steps,
171 divisor_limb);
172 return r >> normalization_steps;
173 }
174 }
175 /* No normalization needed, either because udiv_qrnnd doesn't require
176 * it, or because DIVISOR_LIMB is already normalized. */
177 i = dividend_size - 1;
178 r = dividend_ptr[i];
179
180 if (r >= divisor_limb)
181 r = 0;
182 else
183 i--;
184
185 for (; i >= 0; i--) {
186 n0 = dividend_ptr[i];
187 udiv_qrnnd(dummy, r, r, n0, divisor_limb);
188 }
189 return r;
190 }
191 }
192
193 /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
194 * the NSIZE-DSIZE least significant quotient limbs at QP
195 * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
196 * non-zero, generate that many fraction bits and append them after the
197 * other quotient limbs.
198 * Return the most significant limb of the quotient, this is always 0 or 1.
199 *
200 * Preconditions:
201 * 0. NSIZE >= DSIZE.
202 * 1. The most significant bit of the divisor must be set.
203 * 2. QP must either not overlap with the input operands at all, or
204 * QP + DSIZE >= NP must hold true. (This means that it's
205 * possible to put the quotient in the high part of NUM, right after the
206 * remainder in NUM.
207 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.
208 */
209
210 mpi_limb_t
211 mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,
212 mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)
213 {
214 mpi_limb_t most_significant_q_limb = 0;
215
216 switch (dsize) {
217 case 0:
218 /* We are asked to divide by zero, so go ahead and do it! (To make
219 the compiler not remove this statement, return the value.) */
220 return 1 / dsize;
221
222 case 1:
223 {
224 mpi_size_t i;
225 mpi_limb_t n1;
226 mpi_limb_t d;
227
228 d = dp[0];
229 n1 = np[nsize - 1];
230
231 if (n1 >= d) {
232 n1 -= d;
233 most_significant_q_limb = 1;
234 }
235
236 qp += qextra_limbs;
237 for (i = nsize - 2; i >= 0; i--)
238 udiv_qrnnd(qp[i], n1, n1, np[i], d);
239 qp -= qextra_limbs;
240
241 for (i = qextra_limbs - 1; i >= 0; i--)
242 udiv_qrnnd(qp[i], n1, n1, 0, d);
243
244 np[0] = n1;
245 }
246 break;
247
248 case 2:
249 {
250 mpi_size_t i;
251 mpi_limb_t n1, n0, n2;
252 mpi_limb_t d1, d0;
253
254 np += nsize - 2;
255 d1 = dp[1];
256 d0 = dp[0];
257 n1 = np[1];
258 n0 = np[0];
259
260 if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {
261 sub_ddmmss(n1, n0, n1, n0, d1, d0);
262 most_significant_q_limb = 1;
263 }
264
265 for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {
266 mpi_limb_t q;
267 mpi_limb_t r;
268
269 if (i >= qextra_limbs)
270 np--;
271 else
272 np[0] = 0;
273
274 if (n1 == d1) {
275 /* Q should be either 111..111 or 111..110. Need special
276 * treatment of this rare case as normal division would
277 * give overflow. */
278 q = ~(mpi_limb_t) 0;
279
280 r = n0 + d1;
281 if (r < d1) { /* Carry in the addition? */
282 add_ssaaaa(n1, n0, r - d0,
283 np[0], 0, d0);
284 qp[i] = q;
285 continue;
286 }
287 n1 = d0 - (d0 != 0 ? 1 : 0);
288 n0 = -d0;
289 } else {
290 udiv_qrnnd(q, r, n1, n0, d1);
291 umul_ppmm(n1, n0, d0, q);
292 }
293
294 n2 = np[0];
295 q_test:
296 if (n1 > r || (n1 == r && n0 > n2)) {
297 /* The estimated Q was too large. */
298 q--;
299 sub_ddmmss(n1, n0, n1, n0, 0, d0);
300 r += d1;
301 if (r >= d1) /* If not carry, test Q again. */
302 goto q_test;
303 }
304
305 qp[i] = q;
306 sub_ddmmss(n1, n0, r, n2, n1, n0);
307 }
308 np[1] = n1;
309 np[0] = n0;
310 }
311 break;
312
313 default:
314 {
315 mpi_size_t i;
316 mpi_limb_t dX, d1, n0;
317
318 np += nsize - dsize;
319 dX = dp[dsize - 1];
320 d1 = dp[dsize - 2];
321 n0 = np[dsize - 1];
322
323 if (n0 >= dX) {
324 if (n0 > dX
325 || mpihelp_cmp(np, dp, dsize - 1) >= 0) {
326 mpihelp_sub_n(np, np, dp, dsize);
327 n0 = np[dsize - 1];
328 most_significant_q_limb = 1;
329 }
330 }
331
332 for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {
333 mpi_limb_t q;
334 mpi_limb_t n1, n2;
335 mpi_limb_t cy_limb;
336
337 if (i >= qextra_limbs) {
338 np--;
339 n2 = np[dsize];
340 } else {
341 n2 = np[dsize - 1];
342 MPN_COPY_DECR(np + 1, np, dsize - 1);
343 np[0] = 0;
344 }
345
346 if (n0 == dX) {
347 /* This might over-estimate q, but it's probably not worth
348 * the extra code here to find out. */
349 q = ~(mpi_limb_t) 0;
350 } else {
351 mpi_limb_t r;
352
353 udiv_qrnnd(q, r, n0, np[dsize - 1], dX);
354 umul_ppmm(n1, n0, d1, q);
355
356 while (n1 > r
357 || (n1 == r
358 && n0 > np[dsize - 2])) {
359 q--;
360 r += dX;
361 if (r < dX) /* I.e. "carry in previous addition?" */
362 break;
363 n1 -= n0 < d1;
364 n0 -= d1;
365 }
366 }
367
368 /* Possible optimization: We already have (q * n0) and (1 * n1)
369 * after the calculation of q. Taking advantage of that, we
370 * could make this loop make two iterations less. */
371 cy_limb = mpihelp_submul_1(np, dp, dsize, q);
372
373 if (n2 != cy_limb) {
374 mpihelp_add_n(np, np, dp, dsize);
375 q--;
376 }
377
378 qp[i] = q;
379 n0 = np[dsize - 1];
380 }
381 }
382 }
383
384 return most_significant_q_limb;
385 }
386
387 /****************
388 * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
389 * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
390 * Return the single-limb remainder.
391 * There are no constraints on the value of the divisor.
392 *
393 * QUOT_PTR and DIVIDEND_PTR might point to the same limb.
394 */
395
396 mpi_limb_t
397 mpihelp_divmod_1(mpi_ptr_t quot_ptr,
398 mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,
399 mpi_limb_t divisor_limb)
400 {
401 mpi_size_t i;
402 mpi_limb_t n1, n0, r;
403 int dummy;
404
405 if (!dividend_size)
406 return 0;
407
408 /* If multiplication is much faster than division, and the
409 * dividend is large, pre-invert the divisor, and use
410 * only multiplications in the inner loop.
411 *
412 * This test should be read:
413 * Does it ever help to use udiv_qrnnd_preinv?
414 * && Does what we save compensate for the inversion overhead?
415 */
416 if (UDIV_TIME > (2 * UMUL_TIME + 6)
417 && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {
418 int normalization_steps;
419
420 count_leading_zeros(normalization_steps, divisor_limb);
421 if (normalization_steps) {
422 mpi_limb_t divisor_limb_inverted;
423
424 divisor_limb <<= normalization_steps;
425
426 /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
427 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
428 * most significant bit (with weight 2**N) implicit.
429 */
430 /* Special case for DIVISOR_LIMB == 100...000. */
431 if (!(divisor_limb << 1))
432 divisor_limb_inverted = ~(mpi_limb_t) 0;
433 else
434 udiv_qrnnd(divisor_limb_inverted, dummy,
435 -divisor_limb, 0, divisor_limb);
436
437 n1 = dividend_ptr[dividend_size - 1];
438 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);
439
440 /* Possible optimization:
441 * if (r == 0
442 * && divisor_limb > ((n1 << normalization_steps)
443 * | (dividend_ptr[dividend_size - 2] >> ...)))
444 * ...one division less...
445 */
446 for (i = dividend_size - 2; i >= 0; i--) {
447 n0 = dividend_ptr[i];
448 UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r,
449 ((n1 << normalization_steps)
450 | (n0 >>
451 (BITS_PER_MPI_LIMB -
452 normalization_steps))),
453 divisor_limb,
454 divisor_limb_inverted);
455 n1 = n0;
456 }
457 UDIV_QRNND_PREINV(quot_ptr[0], r, r,
458 n1 << normalization_steps,
459 divisor_limb, divisor_limb_inverted);
460 return r >> normalization_steps;
461 } else {
462 mpi_limb_t divisor_limb_inverted;
463
464 /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
465 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
466 * most significant bit (with weight 2**N) implicit.
467 */
468 /* Special case for DIVISOR_LIMB == 100...000. */
469 if (!(divisor_limb << 1))
470 divisor_limb_inverted = ~(mpi_limb_t) 0;
471 else
472 udiv_qrnnd(divisor_limb_inverted, dummy,
473 -divisor_limb, 0, divisor_limb);
474
475 i = dividend_size - 1;
476 r = dividend_ptr[i];
477
478 if (r >= divisor_limb)
479 r = 0;
480 else
481 quot_ptr[i--] = 0;
482
483 for (; i >= 0; i--) {
484 n0 = dividend_ptr[i];
485 UDIV_QRNND_PREINV(quot_ptr[i], r, r,
486 n0, divisor_limb,
487 divisor_limb_inverted);
488 }
489 return r;
490 }
491 } else {
492 if (UDIV_NEEDS_NORMALIZATION) {
493 int normalization_steps;
494
495 count_leading_zeros(normalization_steps, divisor_limb);
496 if (normalization_steps) {
497 divisor_limb <<= normalization_steps;
498
499 n1 = dividend_ptr[dividend_size - 1];
500 r = n1 >> (BITS_PER_MPI_LIMB -
501 normalization_steps);
502
503 /* Possible optimization:
504 * if (r == 0
505 * && divisor_limb > ((n1 << normalization_steps)
506 * | (dividend_ptr[dividend_size - 2] >> ...)))
507 * ...one division less...
508 */
509 for (i = dividend_size - 2; i >= 0; i--) {
510 n0 = dividend_ptr[i];
511 udiv_qrnnd(quot_ptr[i + 1], r, r,
512 ((n1 << normalization_steps)
513 | (n0 >>
514 (BITS_PER_MPI_LIMB -
515 normalization_steps))),
516 divisor_limb);
517 n1 = n0;
518 }
519 udiv_qrnnd(quot_ptr[0], r, r,
520 n1 << normalization_steps,
521 divisor_limb);
522 return r >> normalization_steps;
523 }
524 }
525 /* No normalization needed, either because udiv_qrnnd doesn't require
526 * it, or because DIVISOR_LIMB is already normalized. */
527 i = dividend_size - 1;
528 r = dividend_ptr[i];
529
530 if (r >= divisor_limb)
531 r = 0;
532 else
533 quot_ptr[i--] = 0;
534
535 for (; i >= 0; i--) {
536 n0 = dividend_ptr[i];
537 udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb);
538 }
539 return r;
540 }
541 }
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